Stability of a liquid metal interface affected by a high-frequency magnetic field

Ch. Karcher¹ - J.-U. Mohring²

¹ Department of Mechanical Engineering Technische Universit\E4t Ilmenau, P.O. Box 100565, 98684 Ilmenau, Germany
² Department of Electroheat Technische Universit\E4t Ilmenau, P.O. Box 100565, 98684 Ilmenau, Germany

Abstract
The stability of a free liquid metal surface influenced by an alternating magnetic field is investigated both experimentally and analytically. The experimental set-up consists of an annulus filled with liquid metal GaInSn (Galinstan). The test liquid is observed by a high-speed camera system. The magnetic field of variable frequency is generated by a ring-like inductor located at some distance above the free surface. We observe three kinds of surface instabilities. First, at a certain critical value of the inductor current, a long-wavelength instability is observed. At a slightly higher value, we observe the formation of surface waves, the wavelength of which equals to the skin depth of the induced magnetic field. Eventually, as the amplitude of the waves is likewise of the order of the skin depth, an electromagnetic pinch is observed. A simple analytical model is presented to predict the instability of a flat liquid metal surface affected by an alternating electromagnetic field. The governing equations are simplified by applying both the Hele-Shaw and skin depth approximation. The critical inductor current predicted by the model is in good agreement with the critical value of the first long-wavelength instability observed in experiments. Figs 7, Refs 11.